The concept of infinite sets is mind boggling. A demonstration of how an infinite set would accommodate an infinite subset was illustrated as 'The Grand Hotel.' In the illustration, a hotel with an infinite number of rooms receives an infinite number of guests. The author uses room numbers, and seat assignments in the endless number of carriages, each with an endless number of seats, arriving to drop off the endless number of visitors, in logical combination, to demonstrate how one might continually move guests who already have assigned rooms so the lower numbered rooms can be filled by the never-ending line of guests. Of course, the hotel will never run out of room despite that it is also always full.
That seems like it would take a lot of time. Though you get to see the numbers growing in the concept, it seems like it would be more efficient to just send the first guest as they continue never beginning arriving down the endless hall to the final room that will never exist. Of course, you'd probably want to start building the hotel at that end, so the first room that was passed will never really exist, but, by the time it's needed, the workmen will never have arrived at the other end to even begin the project.
It would save a lot of money on labor and construction, plus you'd save all the time wasted shifting rooms and assigning numbers.
When you consider only the time saved 'not counting,' which too would be infinite, it would make no difference in how much time is left as there would still be an infinite amount left regardless if an infinite amount of it is subtracted, nor would it make any difference if an infinite amount is added, to it.
The point is, regardless of how you do it, you're only going to make what you collect upon arrival. That HAS TO BE considered in the business plan!
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